Metacircular evaluator
An interpreter for a language, written in that same language — the clearest mirror a language can hold up to itself.
A metacircular evaluator is an interpreter for a language written in that same language. The most famous is the half-page of Lisp that defines Lisp's own eval — the heart of John McCarthy's 1960 paper, and the centrepiece of the textbook Structure and Interpretation of Computer Programs.
It sounds like a magic trick, and in a way it is: to read it is to watch a language explain itself to itself, with no remainder. Alan Kay called it "the Maxwell's equations of software" — a tiny set of expressions from which a whole computational universe unfolds.
The metacircular evaluator depends on code being data: you can only write an interpreter so compactly when programs are values your program can take apart. It's the purest demonstration of what homoiconicity buys you.